The present invention generally relates to frequency synchronizers for digital communications systems, and more particularly, to frequency synchronizers that are based on the maximum likelihood criterion from estimation theory and that can achieve both frequency acquisition and frequency tracking without requiring knowledge at the receiver of the carrier's phase angle, baud timing, or a preamble consisting of known signal symbols.
All digital communications systems operate on the basis of a finite number of possible waveforms available for transmission during any particular signaling interval. The digital receivers must process versions of these transmitted waveforms which are corrupted by noise, channel fading, multipath, distortion, unintentional interference, and jamming, for example. The receiver's task is to determine which was the transmitted waveform for a particular signaling interval. Acceptable performance requires that this determination be achieved with high probability of correctness.
The degree of success potentially achievable by a digital communications system depends on the accuracy of reference signals at the receiver in their representation of the possible transmitted waveforms, as they would appear at the receiver, including the effects of noise, etc. To a large degree, achieving good reference signals is synonymous with having the receiver be synchronized with the transmitted waveforms arriving over a transmission channel.
Synchronization in a particular case may involve several parameters. For example, the receiver's reference signals should be based on the correct carrier frequency, which may be unknown due to oscillator drifts or doppler shifts. For best performance, the receiver should have a timing reference to know the beginning of each signaling waveform. For Time-Division-Multiplex (TDM) and/or Time-Division-Multiple Access (TDMA) systems, the level of timing information must be extended to knowing the beginning of groups of time slots (frame synchronization). In order to have the performance improvement potentially available from coherent detection; the receiver requires accurate knowledge of the carrier's phase angle (phase synchronization). For spread-spectrum systems, synchronization to a hopping-frequency pattern and/or a spread-spectrum code sequence is required. For all levels of synchronization, typically the receiver's synchronizers are required to provide good estimates of the unknowns (frequency, phase, timing, etc.) during an initial start-up period (so-called “acquisition”) and to continue to provide good estimates as the system proceeds to operate (so-called “tracking”).
Two general approaches have been useful for designing synchronizers for digital receivers. Many existing synchronizers are based on good engineering reasoning as to what can work (so-called “ad hoc” procedures), as opposed to being mathematically derived based on various math models and theoretical reasoning. Synchronizers of the latter type typically are derived, and implemented, by using the tools of Estimation Theory based upon the Maximum-Likelihood criterion of goodness (maximization of appropriate conditional probability density functions).
The choice and/or design of synchronizers for a particular system greatly depends on the digital modulation technique to be employed and the channel over which the communication is to take place. Practical solutions have long existed for conventional digital modulation techniques such as Phase Shift Key (PSK), Frequency Shift Key (FSK), Amplitude Shift Key (ASK), and Quadrature Amplitude Modulation (QAM), particularly for the case of a Gaussian noise channel. To meet requirements of transmitting data at high rates, with high accuracy, and with minimal bandwidth usage, newer digital signaling techniques have been found. These include Trellis-Coded Modulation (TCM) and Continuous-Phase Modulation (CPM). Generally, the synchronizers for the older, conventional digital receivers are inadequate for the newer techniques. In fact, there are many theoretical versions (special cases) of the energy-efficient and bandwidth-efficient CPM which would be preferred choices for applications but for the lack of good, achievable synchronizers. Since general solutions are unknown, each category of CPM requires finding specialized solutions for the synchronizer designs required for system operation.
An existing system for which better synchronizers are desirable is a special version of CPM known as dual-h, 4-ary, full-response. The meaning of these terms follows from the mathematical model of a signal having the specified CPM waveform, s(t), given below.       s    ⁡          (      t      )        =                              2          ⁢                      E            s                          T              ⁢          ⅇ              jΨ        ⁡                  (                      t            ,                          α              _                                )                    with Es representing the waveform's energy over its interval T, and Ψ(t,α) is the phase function. The function Ψ(t,α) depends on the data sequence α=( - - - αi−1,αi,αi+1, - - - ) where each of the data symbols is randomly and independently selected from the four possibilities (±1, ±3), hence “4-ary.” Also, Ψ(t,α) depends on two constants h0 and h1, called “modulation indexes,” and a function q(t), called the “phase response function,” as follows.       Ψ    ⁡          (              t        ,                  α          _                    )        =            2      ⁢      π      ⁢                          ⁢              h        0            ⁢                        ∑          i                ⁢                                  ⁢                              α                          2              ⁢              i                                ⁢                      q            ⁡                          (                              t                -                                  2                  ⁢                  iT                                            )                                            +          2      ⁢      π      ⁢                          ⁢              h        1            ⁢                        ∑          i                ⁢                                  ⁢                              α                                          2                ⁢                i                            +              1                                ⁢                      q            ⁡                          (                              t                -                                  2                  ⁢                  i                                -                T                            )                                          For “full response” CPM, the function q(t), is as shown in FIG. 1.
A method for synchronizing for the above CPM waveform case requires transmitting a preamble at the beginning of a message. The preamble is a sequence of non-data symbols, known to the receiver. This preamble sequence is transmitted by means of a modulation technique, less complex than the CPM used for data, called Minimum Shift Key (MSK). However, this method of synchronization has certain undesirable characteristics. For example, the requirement that a start-up interval be set aside for a known preamble means a reduction in information rate. A serious problem arises if the receiver is unable to detect the preamble, thus leading to the loss of the follow-on message. Another potential problem of great concern when operating in the presence of an adversary is that the use of a different modulation for a preamble from that for data offers the adversary significant information useful for a jamming attack.
Therefore, a need exists for synchronization processors/circuits that operate without a preamble and without changing modulation methods within a transmission.